Final answer:
The plastic will float because its density (0.849 g/cm³) is less than the density of water (1 g/cm³). For the polystyrene cube, 10% submerged indicates a density less than water, and an additional mass changes the floating percentage to 60% above water, assuming no change in the total volume.
Step-by-step explanation:
To determine if the plastic will float, we can use the concept of density and Archimedes' Principle. The density of water is 1 g/cm³ (or 1000 kg/m³). To float, an object must have a density less than the fluid it is submerged in. We calculate the density of the plastic by dividing its mass by its volume:
Density = Mass / Volume
= 200 g / 235.54 cm³
= 0.849 g/cm³
Since the density of the plastic is less than that of water, the plastic will float on water regardless of its shape. Therefore, the answer is (a) Yes.
Problem 3
a. If 90% of the polystyrene cube is above the water, that means 10% is submerged. Using the principle that the buoyant force equals the weight of the displaced fluid, we can find the density of polystyrene as follows:
Calculate the volume of the submerged part: 10% of the full volume.
Volume of submerged part = 0.10 x (10 cm x 10 cm x 10 cm) = 100 cm³.
Weight of displaced water = density of water x volume of submerged part.
Density of polystyrene = mass of polystyrene / volume of submerged part.
Given that the polystyrene cube is not sinking, its density must be less than water, but to find the exact value, we would need the mass of the cube. However, based on the information provided in a reference answer, the density is 100 kg/m³.
b. When a 0.5 kg mass is placed on the polystyrene, the additional weight causes more of the polystyrene to submerge to displace enough water to equal the new total weight (polystyrene + mass). The reference answer indicates that now 60% of the block remains above water.